2nd/10_Wiki/Topics/AI_and_ML/Replenishment.md

---
id: wiki-2026-0508-replenishment
title: Replenishment
category: 10_Wiki/Topics
status: verified
canonical_id: self
aliases: [Inventory Replenishment, Stock Replenishment, 재고보충]
duplicate_of: none
source_trust_level: A
confidence_score: 0.9
verification_status: applied
tags: [supply-chain, inventory, operations, forecasting, optimization]
raw_sources: []
last_reinforced: 2026-05-10
github_commit: pending
tech_stack:
  language: Python
  framework: pandas/scipy/forecasting
---

# Replenishment

## 매 한 줄
> **"매 right item, right quantity, right time."**. Replenishment 매 inventory 가 demand 의 동안 stockout 의 X 의 process 의 maintaining. 1934 Wilson EOQ 부터 modern AI-driven probabilistic forecasting (Amazon, Walmart 의 LSTM/Transformer demand models) 까지 evolved.

## 매 핵심

### 매 핵심 levers
- **Reorder Point (ROP)**: trigger threshold = `lead_time_demand + safety_stock`.
- **Order Quantity**: how much (EOQ, min-max, fixed).
- **Review period**: continuous (Q-system) 의 X periodic (P-system).
- **Safety Stock**: buffer 의 demand/lead-time variability 의.

### 매 modern signals
- Probabilistic demand forecast (quantiles, 의 X point estimate).
- Lead time variance (supplier reliability score).
- Cross-location pooling (omnichannel inventory).
- Substitution + promotion lift modeling.

### 매 응용
1. Retail (Walmart, Costco 의 daily auto-replenishment).
2. E-commerce FBA (Amazon 의 fulfillment center distribution).
3. Manufacturing MRP (BOM-driven component replenishment).
4. Healthcare (vaccine, drug 의 cold-chain replenishment).

## 💻 패턴

### EOQ (Economic Order Quantity)
```python
import math

def eoq(annual_demand: float, order_cost: float, holding_cost_per_unit: float) -> float:
    """Wilson formula. Min total cost = order + holding."""
    return math.sqrt(2 * annual_demand * order_cost / holding_cost_per_unit)

# Example: 10K units/yr, $50/order, $2/unit/yr holding
print(eoq(10_000, 50, 2))  # 707 units per order
```

### Reorder Point with Safety Stock
```python
from scipy.stats import norm

def reorder_point(daily_demand_mean, daily_demand_std,
                  lead_time_days, service_level=0.95):
    z = norm.ppf(service_level)
    lead_time_demand = daily_demand_mean * lead_time_days
    safety_stock = z * daily_demand_std * math.sqrt(lead_time_days)
    return lead_time_demand + safety_stock, safety_stock
```

### Min-Max (s, S) Policy
```python
def min_max_order(on_hand: int, on_order: int, s: int, S: int) -> int:
    """매 inventory_position <= s 일 때 S 까지 order."""
    inv_pos = on_hand + on_order
    return max(0, S - inv_pos) if inv_pos <= s else 0
```

### Probabilistic Forecast → Newsvendor
```python
import numpy as np

def newsvendor_quantile(unit_cost, sale_price, salvage=0):
    """Critical ratio = (p - c) / (p - s)."""
    return (sale_price - unit_cost) / (sale_price - salvage)

def order_qty_from_forecast(demand_samples: np.ndarray, critical_ratio: float):
    return float(np.quantile(demand_samples, critical_ratio))

# 1000 Monte Carlo demand samples → optimal order
samples = np.random.gamma(shape=4, scale=25, size=1000)
cr = newsvendor_quantile(unit_cost=10, sale_price=25, salvage=3)
print(order_qty_from_forecast(samples, cr))
```

### LSTM Demand Forecast (modern)
```python
import torch.nn as nn

class DemandLSTM(nn.Module):
    def __init__(self, n_features=8, hidden=64):
        super().__init__()
        self.lstm = nn.LSTM(n_features, hidden, num_layers=2,
                            dropout=0.2, batch_first=True)
        self.head = nn.Linear(hidden, 3)  # P10, P50, P90 quantiles

    def forward(self, x):
        out, _ = self.lstm(x)
        return self.head(out[:, -1])
```

### Multi-Echelon Allocation
```python
def fair_share_allocation(forecasts: dict, total_supply: float) -> dict:
    """Allocate constrained supply across stores proportional to forecast."""
    total_demand = sum(forecasts.values())
    if total_supply >= total_demand:
        return forecasts.copy()
    ratio = total_supply / total_demand
    return {loc: f * ratio for loc, f in forecasts.items()}
```

### KPI Dashboard
```python
def replenishment_kpis(history: list[dict]) -> dict:
    stockouts = sum(1 for d in history if d["on_hand"] == 0)
    fill_rate = sum(d["fulfilled"] for d in history) / sum(d["demanded"] for d in history)
    avg_inv = sum(d["on_hand"] for d in history) / len(history)
    return {
        "service_level": 1 - stockouts / len(history),
        "fill_rate": fill_rate,
        "avg_inventory": avg_inv,
        "inventory_turns": sum(d["demanded"] for d in history) / avg_inv,
    }
```

## 매 결정 기준
| 상황 | Approach |
|---|---|
| Stable demand, known lead time | EOQ + ROP |
| Highly variable demand | Probabilistic forecast + newsvendor |
| Many SKUs, low value | Min-Max (s, S) |
| Perishable / fashion | Newsvendor (single-period) |
| Multi-location, constrained supply | Fair-share / DRP |
| Modern e-commerce scale | ML demand model + RL ordering policy |

**기본값**: Probabilistic LSTM forecast → newsvendor quantile order. 매 P50 forecast + ROP 의 단순 baseline 의 X.

## 🔗 Graph
- 부모: [[Supply Chain Management]] · [[Operations Research]]
- Adjacent: [[Reinforcement Learning]] · [[MRP]]

## 🤖 LLM 활용
**언제**: SKU master data 의 cleansing, supplier email parsing, anomaly explanation, what-if scenario 의 narrative.
**언제 X**: 매 actual demand forecasting 의 LLM 의 X — purpose-built time-series models (Prophet, NeuralForecast, Chronos) 의 use.

## ❌ 안티패턴
- **Point forecast only**: P50 만 사용 의 X — quantiles 의 사용 의 service level tuning 의 가능.
- **Static safety stock**: lead time 의 variance 의 ignore 의 X.
- **Local optimization**: 각 store 의 independent ordering — pooling 의 lost.
- **Bullwhip ignored**: downstream order 의 upstream 의 amplification 의 monitor 의 필요.
- **Excel-only**: 1000+ SKU 의 manual review 의 scale 의 X.

## 🧪 검증 / 중복
- Verified (Silver/Pyke "Inventory Management" textbook, AWS Forecast docs).
- 신뢰도 A.

## 🕓 Changelog
| 날짜 | 변경 |
|---|---|
| 2026-05-08 | Phase 1 |
| 2026-05-10 | Manual cleanup — replenishment policy + ML forecasting patterns |